Problem: Solve for $x$, $- \dfrac{3x + 4}{4x + 1} = \dfrac{1}{7} $
Solution: Multiply both sides of the equation by $4x + 1$ $ -(3x + 4) = \dfrac{4x + 1}{7} $ Multiply both sides of the equation by $7$ $ -7(3x + 4) = 4x + 1 $ $-21x - 28 = 4x + 1$ $-28 = 25x + 1$ $-29 = 25x$ $25x = -29$ $x = -\dfrac{29}{25}$